What could cause an object disapear only in Edit Mode?
shift+t moves object's texture space - it has nothing to do with visibility. 

You may have some modifier the effects of which is not visible in edit mode, or, more likely, you hid everything with h. To unhide the geometry hidden, you can go to edit mode and hit alt+h to unhide everything. 

To reset the location of object's texture space if you moved it accidentally, you can set the values to 0 in the Properties Editor, Mesh tab, under Texture Space: